Problem: What do the following two equations represent? $3x-3y = 4$ $6x+6y = -2$
Putting the first equation in $y = mx + b$ form gives: $3x-3y = 4$ $-3y = -3x+4$ $y = 1x - \dfrac{4}{3}$ Putting the second equation in $y = mx + b$ form gives: $6x+6y = -2$ $6y = -6x-2$ $y = -1x - \dfrac{1}{3}$ The slopes are negative inverses of each other, so the lines are perpendicular.